Solve for x 5x^2+43=(x-1)(5x+6)

$5 x^{2} + 43 = (x - 1) (5 x + 6)$

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$(x - 1) (5 x + 6) = 5 x^{2} + 43$

Simplify $(x - 1) (5 x + 6)$ .

Rewrite.

$0 + 0 + (x - 1) (5 x + 6) = 5 x^{2} + 43$

Simplify by adding zeros.

$(x - 1) (5 x + 6) = 5 x^{2} + 43$

Expand $(x - 1) (5 x + 6)$ using the FOIL Method.

Apply the distributive property.

$x (5 x + 6) - 1 (5 x + 6) = 5 x^{2} + 43$

Apply the distributive property.

$x (5 x) + x \cdot 6 - 1 (5 x + 6) = 5 x^{2} + 43$

Apply the distributive property.

$x (5 x) + x \cdot 6 - 1 (5 x) - 1 \cdot 6 = 5 x^{2} + 43$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 x \cdot x + x \cdot 6 - 1 (5 x) - 1 \cdot 6 = 5 x^{2} + 43$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$5 (x \cdot x) + x \cdot 6 - 1 (5 x) - 1 \cdot 6 = 5 x^{2} + 43$

Multiply $x$ by $x$ .

$5 x^{2} + x \cdot 6 - 1 (5 x) - 1 \cdot 6 = 5 x^{2} + 43$

Move $6$ to the left of $x$ .

$5 x^{2} + 6 \cdot x - 1 (5 x) - 1 \cdot 6 = 5 x^{2} + 43$

Multiply $5$ by $- 1$ .

$5 x^{2} + 6 x - 5 x - 1 \cdot 6 = 5 x^{2} + 43$

Multiply $- 1$ by $6$ .

$5 x^{2} + 6 x - 5 x - 6 = 5 x^{2} + 43$

Subtract $5 x$ from $6 x$ .

$5 x^{2} + x - 6 = 5 x^{2} + 43$

Move all terms containing $x$ to the left side of the equation.

Subtract $5 x^{2}$ from both sides of the equation.

$5 x^{2} + x - 6 - 5 x^{2} = 43$

Combine the opposite terms in $5 x^{2} + x - 6 - 5 x^{2}$ .

Subtract $5 x^{2}$ from $5 x^{2}$ .

$x - 6 + 0 = 43$

Add $x - 6$ and $0$ .

$x - 6 = 43$

Move all terms not containing $x$ to the right side of the equation.

Add $6$ to both sides of the equation.

$x = 43 + 6$

Add $43$ and $6$ .

$x = 49$