Solve 12a ^ 3 + 4a ^ 2 + 3a + 8 - x = 16a ^ 3 - 6a ^ 2 + 5a + 11 | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$12a^{3}+4a^{2}+3a+8-x=16a^{3}-6a^{2}+5a+11$$

Solve for x

$x=-4a^{3}+10a^{2}-2a-3$

Steps for Solving Linear Equation

Subtract $12a^{3}$ from both sides.

$$4a^{2}+3a+8-x=16a^{3}-6a^{2}+5a+11-12a^{3}$$

Combine $16a^{3}$ and $-12a^{3}$ to get $4a^{3}$.

$$4a^{2}+3a+8-x=4a^{3}-6a^{2}+5a+11$$

Subtract $4a^{2}$ from both sides.

$$3a+8-x=4a^{3}-6a^{2}+5a+11-4a^{2}$$

Combine $-6a^{2}$ and $-4a^{2}$ to get $-10a^{2}$.

$$3a+8-x=4a^{3}-10a^{2}+5a+11$$

Subtract $3a$ from both sides.

$$8-x=4a^{3}-10a^{2}+5a+11-3a$$

Combine $5a$ and $-3a$ to get $2a$.

$$8-x=4a^{3}-10a^{2}+2a+11$$

Subtract $8$ from both sides.

$$-x=4a^{3}-10a^{2}+2a+11-8$$

Subtract $8$ from $11$ to get $3$.

$$-x=4a^{3}-10a^{2}+2a+3$$

Divide both sides by $-1$.

$$\frac{-x}{-1}=\frac{4a^{3}-10a^{2}+2a+3}{-1}$$

Dividing by $-1$ undoes the multiplication by $-1$.

$$x=\frac{4a^{3}-10a^{2}+2a+3}{-1}$$

Divide $4a^{3}-10a^{2}+2a+3$ by $-1$.

$$x=-4a^{3}+10a^{2}-2a-3$$